<img src="https://tex.z-dn.net/?f=p%3DdF%2FdA%20%5Cto%20dF%3DpdA%2F%2F%20F%3Dmg%20%5Cto%20dF%3Dgdm%20%5Cto%20gdm%3DpdA%0A" />
<img src="https://tex.z-dn.net/?f=dm%3D%5Cfrac%7Bp%7D%7Bg%7DdA%20%5Cto%20m%3D%20%5Cfrac%7Bp%7D%7Bg%7D%5Cint%5Climits_S%20%5C%2C%20dA%20%5Cto%20m%3D%5Cfrac%7Bp%7D%7Bg%7DS" />
S representa la superficie de la tierra, aproximada a una esfera se tiene :
<img src="https://tex.z-dn.net/?f=S%3D4%5Cpi%20r%5E2%20%5Cto%20m%3D4%5Cpi%5Cfrac%7Bp%7D%7Bg%7D%20r%5E2" />
Sustituyendo los valores (recordemos que 1atm = 98000 Pa)
<img src="https://tex.z-dn.net/?f=m%3D%204%5Cpi%5Cfrac%7B98000Pa%7D%7B9.8m%2Fs%5E2%7D%286.38%2A10%5E5m%29%5E2%20%5Cto%20%5Cboldsymbol%7Bm%3D5%2C115%2A%2010%5E%7B16%7Dkg%7D" />.